LMFDB - Embedded newform 1050.3.c.c.449.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(449,1050)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1050.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.25
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.c.449.26

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(1.60951 - 2.53169i) q^{3} +2.00000 q^{4} +(2.27619 - 3.58035i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(-3.81894 - 8.14958i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(1.60951 - 2.53169i) q^{3} +2.00000 q^{4} +(2.27619 - 3.58035i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(-3.81894 - 8.14958i) q^{9} +13.4366i q^{11} +(3.21903 - 5.06339i) q^{12} -19.9431i q^{13} -3.74166i q^{14} +4.00000 q^{16} +16.8546 q^{17} +(-5.40079 - 11.5253i) q^{18} +20.2080 q^{19} +(-6.69823 - 4.25837i) q^{21} +19.0022i q^{22} -6.13260 q^{23} +(4.55239 - 7.16071i) q^{24} -28.2039i q^{26} +(-26.7789 - 3.44849i) q^{27} -5.29150i q^{28} -46.5221i q^{29} -17.2147 q^{31} +5.65685 q^{32} +(34.0173 + 21.6264i) q^{33} +23.8359 q^{34} +(-7.63787 - 16.2992i) q^{36} -64.7559i q^{37} +28.5785 q^{38} +(-50.4899 - 32.0987i) q^{39} +62.5496i q^{41} +(-9.47273 - 6.02225i) q^{42} -71.0317i q^{43} +26.8732i q^{44} -8.67280 q^{46} -47.6863 q^{47} +(6.43805 - 10.1268i) q^{48} -7.00000 q^{49} +(27.1276 - 42.6705i) q^{51} -39.8863i q^{52} +36.2448 q^{53} +(-37.8710 - 4.87690i) q^{54} -7.48331i q^{56} +(32.5251 - 51.1605i) q^{57} -65.7922i q^{58} -2.49151i q^{59} +12.5448 q^{61} -24.3453 q^{62} +(-21.5618 + 10.1040i) q^{63} +8.00000 q^{64} +(48.1077 + 30.5843i) q^{66} +118.236i q^{67} +33.7091 q^{68} +(-9.87050 + 15.5259i) q^{69} -7.94718i q^{71} +(-10.8016 - 23.0505i) q^{72} +73.2141i q^{73} -91.5787i q^{74} +40.4161 q^{76} +35.5499 q^{77} +(-71.4035 - 45.3945i) q^{78} -108.171 q^{79} +(-51.8315 + 62.2455i) q^{81} +88.4585i q^{82} +92.8713 q^{83} +(-13.3965 - 8.51674i) q^{84} -100.454i q^{86} +(-117.780 - 74.8779i) q^{87} +38.0044i q^{88} -5.36877i q^{89} -52.7646 q^{91} -12.2652 q^{92} +(-27.7073 + 43.5824i) q^{93} -67.4386 q^{94} +(9.10478 - 14.3214i) q^{96} +8.58686i q^{97} -9.89949 q^{98} +(109.503 - 51.3135i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	$ 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	1.60951	−	2.53169i	0.536504	−	0.843898i
$3$	1.60951	−	2.53169i	0.536504	−	0.843898i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	2.27619	−	3.58035i	0.379366	−	0.596726i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	2.82843			0.353553
$9$	−3.81894	−	8.14958i	−0.424326	−	0.905509i
$10$		0			0
$11$			13.4366i			1.22151i	0.791820	+	0.610754i	$0.209134\pi$
$11$			13.4366i			1.22151i	−0.791820	+	0.610754i	$0.790866\pi$
$12$	3.21903	−	5.06339i	0.268252	−	0.421949i
$13$		−	19.9431i		−	1.53409i	−0.641595	−	0.767044i	$-0.721727\pi$
$13$		−	19.9431i		−	1.53409i	0.641595	−	0.767044i	$-0.278273\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	16.8546			0.991444			0.495722	−	0.868481i	$-0.334903\pi$
$17$	16.8546			0.991444			0.495722	+	0.868481i	$0.334903\pi$
$18$	−5.40079	−	11.5253i	−0.300044	−	0.640292i
$19$	20.2080			1.06358			0.531790	−	0.846876i	$-0.321519\pi$
$19$	20.2080			1.06358			0.531790	+	0.846876i	$0.321519\pi$
$20$		0			0
$21$	−6.69823	−	4.25837i	−0.318963	−	0.202780i
$22$			19.0022i			0.863736i
$23$	−6.13260			−0.266635			−0.133317	−	0.991073i	$-0.542563\pi$
$23$	−6.13260			−0.266635			−0.133317	+	0.991073i	$0.542563\pi$
$24$	4.55239	−	7.16071i	0.189683	−	0.298363i
$25$		0			0
$26$		−	28.2039i		−	1.08476i
$27$	−26.7789	−	3.44849i	−0.991810	−	0.127722i
$28$		−	5.29150i		−	0.188982i
$29$		−	46.5221i		−	1.60421i	−0.597183	−	0.802105i	$-0.703713\pi$
$29$		−	46.5221i		−	1.60421i	0.597183	−	0.802105i	$-0.296287\pi$
$30$		0			0
$31$	−17.2147			−0.555314			−0.277657	−	0.960680i	$-0.589558\pi$
$31$	−17.2147			−0.555314			−0.277657	+	0.960680i	$0.589558\pi$
$32$	5.65685			0.176777
$33$	34.0173	+	21.6264i	1.03083	+	0.655344i
$34$	23.8359			0.701057
$35$		0			0
$36$	−7.63787	−	16.2992i	−0.212163	−	0.452755i
$37$		−	64.7559i		−	1.75016i	−0.483978	−	0.875080i	$-0.660809\pi$
$37$		−	64.7559i		−	1.75016i	0.483978	−	0.875080i	$-0.339191\pi$
$38$	28.5785			0.752065
$39$	−50.4899	−	32.0987i	−1.29461	−	0.823045i
$40$		0			0
$41$			62.5496i			1.52560i	0.646634	+	0.762800i	$0.276176\pi$
$41$			62.5496i			1.52560i	−0.646634	+	0.762800i	$0.723824\pi$
$42$	−9.47273	−	6.02225i	−0.225541	−	0.143387i
$43$		−	71.0317i		−	1.65190i	−0.563744	−	0.825949i	$-0.690640\pi$
$43$		−	71.0317i		−	1.65190i	0.563744	−	0.825949i	$-0.309360\pi$
$44$			26.8732i			0.610754i
$45$		0			0
$46$	−8.67280			−0.188539
$47$	−47.6863			−1.01460			−0.507301	−	0.861769i	$-0.669357\pi$
$47$	−47.6863			−1.01460			−0.507301	+	0.861769i	$0.669357\pi$
$48$	6.43805	−	10.1268i	0.134126	−	0.210974i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	27.1276	−	42.6705i	0.531914	−	0.836677i
$52$		−	39.8863i		−	0.767044i
$53$	36.2448			0.683864			0.341932	−	0.939725i	$-0.388919\pi$
$53$	36.2448			0.683864			0.341932	+	0.939725i	$0.388919\pi$
$54$	−37.8710	−	4.87690i	−0.701316	−	0.0903129i
$55$		0			0
$56$		−	7.48331i		−	0.133631i
$57$	32.5251	−	51.1605i	0.570616	−	0.897553i
$58$		−	65.7922i		−	1.13435i
$59$		−	2.49151i		−	0.0422290i	−0.999777	−	0.0211145i	$-0.993279\pi$
$59$		−	2.49151i		−	0.0422290i	0.999777	−	0.0211145i	$-0.00672145\pi$
$60$		0			0
$61$	12.5448			0.205653			0.102826	−	0.994699i	$-0.467211\pi$
$61$	12.5448			0.205653			0.102826	+	0.994699i	$0.467211\pi$
$62$	−24.3453			−0.392666
$63$	−21.5618	+	10.1040i	−0.342250	+	0.160380i
$64$	8.00000			0.125000
$65$		0			0
$66$	48.1077	+	30.5843i	0.728905	+	0.463398i
$67$			118.236i			1.76471i	0.470581	+	0.882357i	$0.344044\pi$
$67$			118.236i			1.76471i	−0.470581	+	0.882357i	$0.655956\pi$
$68$	33.7091			0.495722
$69$	−9.87050	+	15.5259i	−0.143051	+	0.225012i
$70$		0			0
$71$		−	7.94718i		−	0.111932i	−0.998433	−	0.0559660i	$-0.982176\pi$
$71$		−	7.94718i		−	0.111932i	0.998433	−	0.0559660i	$-0.0178239\pi$
$72$	−10.8016	−	23.0505i	−0.150022	−	0.320146i
$73$			73.2141i			1.00293i	0.865177	+	0.501466i	$0.167206\pi$
$73$			73.2141i			1.00293i	−0.865177	+	0.501466i	$0.832794\pi$
$74$		−	91.5787i		−	1.23755i
$75$		0			0
$76$	40.4161			0.531790
$77$	35.5499			0.461687
$78$	−71.4035	−	45.3945i	−0.915429	−	0.581980i
$79$	−108.171			−1.36925			−0.684627	−	0.728893i	$-0.740035\pi$
$79$	−108.171			−1.36925			−0.684627	+	0.728893i	$0.740035\pi$
$80$		0			0
$81$	−51.8315	+	62.2455i	−0.639894	+	0.768463i
$82$			88.4585i			1.07876i
$83$	92.8713			1.11893			0.559466	−	0.828854i	$-0.311006\pi$
$83$	92.8713			1.11893			0.559466	+	0.828854i	$0.311006\pi$
$84$	−13.3965	−	8.51674i	−0.159482	−	0.101390i
$85$		0			0
$86$		−	100.454i		−	1.16807i
$87$	−117.780	−	74.8779i	−1.35379	−	0.860666i
$88$			38.0044i			0.431868i
$89$		−	5.36877i		−	0.0603233i	−0.999545	−	0.0301616i	$-0.990398\pi$
$89$		−	5.36877i		−	0.0603233i	0.999545	−	0.0301616i	$-0.00960221\pi$
$90$		0			0
$91$	−52.7646			−0.579831
$92$	−12.2652			−0.133317
$93$	−27.7073	+	43.5824i	−0.297928	+	0.468628i
$94$	−67.4386			−0.717432
$95$		0			0
$96$	9.10478	−	14.3214i	0.0948415	−	0.149181i
$97$			8.58686i			0.0885243i	0.999020	+	0.0442621i	$0.0140937\pi$
$97$			8.58686i			0.0885243i	−0.999020	+	0.0442621i	$0.985906\pi$
$98$	−9.89949			−0.101015
$99$	109.503	−	51.3135i	1.10609	−	0.518318i
$100$		0			0
$101$		−	38.8036i		−	0.384194i	−0.981376	−	0.192097i	$-0.938471\pi$
$101$		−	38.8036i		−	0.384194i	0.981376	−	0.192097i	$-0.0615288\pi$
$102$	38.3642	−	60.3453i	0.376120	−	0.591620i
$103$		−	8.45500i		−	0.0820873i	−0.999157	−	0.0410437i	$-0.986932\pi$
$103$		−	8.45500i		−	0.0820873i	0.999157	−	0.0410437i	$-0.0130683\pi$
$104$		−	56.4077i		−	0.542382i
$105$		0			0
$106$	51.2579			0.483565
$107$	54.3515			0.507958			0.253979	−	0.967210i	$-0.418261\pi$
$107$	54.3515			0.507958			0.253979	+	0.967210i	$0.418261\pi$
$108$	−53.5577	−	6.89698i	−0.495905	−	0.0638609i
$109$	102.194			0.937560			0.468780	−	0.883315i	$-0.344694\pi$
$109$	102.194			0.937560			0.468780	+	0.883315i	$0.344694\pi$
$110$		0			0
$111$	−163.942	−	104.225i	−1.47696	−	0.938968i
$112$		−	10.5830i		−	0.0944911i
$113$	135.780			1.20159			0.600797	−	0.799402i	$-0.294850\pi$
$113$	135.780			1.20159			0.600797	+	0.799402i	$0.294850\pi$
$114$	45.9974	−	72.3519i	0.403486	−	0.634666i
$115$		0			0
$116$		−	93.0442i		−	0.802105i
$117$	−162.528	+	76.1616i	−1.38913	+	0.650954i
$118$		−	3.52352i		−	0.0298604i
$119$		−	44.5930i		−	0.374731i
$120$		0			0
$121$	−59.5418			−0.492081
$122$	17.7411			0.145418
$123$	158.356	+	100.674i	1.28745	+	0.818491i
$124$	−34.4295			−0.277657
$125$		0			0
$126$	−30.4930	+	14.2892i	−0.242008	+	0.113406i
$127$			181.101i			1.42599i	0.701167	+	0.712997i	$0.252663\pi$
$127$			181.101i			1.42599i	−0.701167	+	0.712997i	$0.747337\pi$
$128$	11.3137			0.0883883
$129$	−179.830	−	114.326i	−1.39403	−	0.886251i
$130$		0			0
$131$		−	4.01429i		−	0.0306434i	−0.999883	−	0.0153217i	$-0.995123\pi$
$131$		−	4.01429i		−	0.0306434i	0.999883	−	0.0153217i	$-0.00487725\pi$
$132$	68.0346	+	43.2527i	0.515414	+	0.327672i
$133$		−	53.4654i		−	0.401996i
$134$			167.211i			1.24784i
$135$		0			0
$136$	47.6719			0.350528
$137$	78.4136			0.572362			0.286181	−	0.958176i	$-0.407614\pi$
$137$	78.4136			0.572362			0.286181	+	0.958176i	$0.407614\pi$
$138$	−13.9590	+	21.9569i	−0.101152	+	0.159108i
$139$	41.0289			0.295172			0.147586	−	0.989049i	$-0.452850\pi$
$139$	41.0289			0.295172			0.147586	+	0.989049i	$0.452850\pi$
$140$		0			0
$141$	−76.7517	+	120.727i	−0.544338	+	0.856220i
$142$		−	11.2390i		−	0.0791479i
$143$	267.968			1.87390
$144$	−15.2757	−	32.5983i	−0.106082	−	0.226377i
$145$		0			0
$146$			103.540i			0.709180i
$147$	−11.2666	+	17.7218i	−0.0766435	+	0.120557i
$148$		−	129.512i		−	0.875080i
$149$		−	22.0376i		−	0.147903i	−0.997262	−	0.0739515i	$-0.976439\pi$
$149$		−	22.0376i		−	0.147903i	0.997262	−	0.0739515i	$-0.0235610\pi$
$150$		0			0
$151$	−96.2729			−0.637569			−0.318784	−	0.947827i	$-0.603275\pi$
$151$	−96.2729			−0.637569			−0.318784	+	0.947827i	$0.603275\pi$
$152$	57.1569			0.376033
$153$	−64.3665	−	137.358i	−0.420696	−	0.897762i
$154$	50.2751			0.326462
$155$		0			0
$156$	−100.980	−	64.1975i	−0.647306	−	0.411522i
$157$			21.6287i			0.137763i	0.997625	+	0.0688813i	$0.0219430\pi$
$157$			21.6287i			0.137763i	−0.997625	+	0.0688813i	$0.978057\pi$
$158$	−152.977			−0.968209
$159$	58.3365	−	91.7607i	0.366896	−	0.577111i
$160$		0			0
$161$			16.2253i			0.100778i
$162$	−73.3007	+	88.0284i	−0.452474	+	0.543385i
$163$			223.849i			1.37331i	0.726985	+	0.686654i	$0.240921\pi$
$163$			223.849i			1.37331i	−0.726985	+	0.686654i	$0.759079\pi$
$164$			125.099i			0.762800i
$165$		0			0
$166$	131.340			0.791204
$167$	287.979			1.72442			0.862212	−	0.506548i	$-0.169079\pi$
$167$	287.979			1.72442			0.862212	+	0.506548i	$0.169079\pi$
$168$	−18.9455	−	12.0445i	−0.112771	−	0.0716934i
$169$	−228.729			−1.35342
$170$		0			0
$171$	−77.1732	−	164.687i	−0.451305	−	0.963082i
$172$		−	142.063i		−	0.825949i
$173$	−289.069			−1.67092			−0.835458	−	0.549554i	$-0.814798\pi$
$173$	−289.069			−1.67092			−0.835458	+	0.549554i	$0.814798\pi$
$174$	−166.566	−	105.893i	−0.957273	−	0.608582i
$175$		0			0
$176$			53.7463i			0.305377i
$177$	−6.30773	−	4.01011i	−0.0356369	−	0.0226560i
$178$		−	7.59259i		−	0.0426550i
$179$		−	46.6099i		−	0.260391i	−0.991488	−	0.130195i	$-0.958440\pi$
$179$		−	46.6099i		−	0.260391i	0.991488	−	0.130195i	$-0.0415605\pi$
$180$		0			0
$181$	−138.088			−0.762920			−0.381460	−	0.924385i	$-0.624579\pi$
$181$	−138.088			−0.762920			−0.381460	+	0.924385i	$0.624579\pi$
$182$	−74.6204			−0.410002
$183$	20.1911	−	31.7596i	0.110334	−	0.173550i
$184$	−17.3456			−0.0942696
$185$		0			0
$186$	−39.1841	+	61.6349i	−0.210667	+	0.331370i
$187$			226.468i			1.21106i
$188$	−95.3726			−0.507301
$189$	−9.12384	+	70.8502i	−0.0482743	+	0.374869i
$190$		0			0
$191$			19.7131i			0.103210i	0.998668	+	0.0516051i	$0.0164337\pi$
$191$			19.7131i			0.103210i	−0.998668	+	0.0516051i	$0.983566\pi$
$192$	12.8761	−	20.2535i	0.0670630	−	0.105487i
$193$		−	55.0627i		−	0.285299i	−0.989773	−	0.142650i	$-0.954438\pi$
$193$		−	55.0627i		−	0.285299i	0.989773	−	0.142650i	$-0.0455622\pi$
$194$			12.1436i			0.0625961i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	225.696			1.14567			0.572833	−	0.819672i	$-0.305844\pi$
$197$	225.696			1.14567			0.572833	+	0.819672i	$0.305844\pi$
$198$	154.860	−	72.5682i	0.782121	−	0.366506i
$199$	−187.480			−0.942109			−0.471054	−	0.882104i	$-0.656126\pi$
$199$	−187.480			−0.942109			−0.471054	+	0.882104i	$0.656126\pi$
$200$		0			0
$201$	299.337	+	190.302i	1.48924	+	0.946776i
$202$		−	54.8766i		−	0.271666i
$203$	−123.086			−0.606334
$204$	54.2552	−	85.3411i	0.265957	−	0.418339i
$205$		0			0
$206$		−	11.9572i		−	0.0580445i
$207$	23.4200	+	49.9781i	0.113140	+	0.241440i
$208$		−	79.7725i		−	0.383522i
$209$			271.527i			1.29917i
$210$		0			0
$211$	346.309			1.64127			0.820637	−	0.571450i	$-0.193619\pi$
$211$	346.309			1.64127			0.820637	+	0.571450i	$0.193619\pi$
$212$	72.4896			0.341932
$213$	−20.1198	−	12.7911i	−0.0944592	−	0.0600520i
$214$	76.8646			0.359180
$215$		0			0
$216$	−75.7421	−	9.75380i	−0.350658	−	0.0451565i
$217$			45.5459i			0.209889i
$218$	144.524			0.662955
$219$	185.356	+	117.839i	0.846372	+	0.538078i
$220$		0			0
$221$		−	336.133i		−	1.52096i
$222$	−231.849	−	147.397i	−1.04437	−	0.663951i
$223$			316.434i			1.41899i	0.704712	+	0.709494i	$0.251076\pi$
$223$			316.434i			1.41899i	−0.704712	+	0.709494i	$0.748924\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	192.022			0.849655
$227$	−7.78561			−0.0342979			−0.0171489	−	0.999853i	$-0.505459\pi$
$227$	−7.78561			−0.0342979			−0.0171489	+	0.999853i	$0.505459\pi$
$228$	65.0502	−	102.321i	0.285308	−	0.448777i
$229$	121.893			0.532284			0.266142	−	0.963934i	$-0.414251\pi$
$229$	121.893			0.532284			0.266142	+	0.963934i	$0.414251\pi$
$230$		0			0
$231$	57.2180	−	90.0013i	0.247697	−	0.389616i
$232$		−	131.584i		−	0.567174i
$233$	80.1577			0.344024			0.172012	−	0.985095i	$-0.444973\pi$
$233$	80.1577			0.344024			0.172012	+	0.985095i	$0.444973\pi$
$234$	−229.850	+	107.709i	−0.982264	+	0.460294i
$235$		0			0
$236$		−	4.98302i		−	0.0211145i
$237$	−174.103	+	273.856i	−0.734611	+	1.15551i
$238$		−	63.0640i		−	0.264975i
$239$			116.255i			0.486424i	0.969973	+	0.243212i	$0.0782011\pi$
$239$			116.255i			0.486424i	−0.969973	+	0.243212i	$0.921799\pi$
$240$		0			0
$241$	94.7516			0.393160			0.196580	−	0.980488i	$-0.437016\pi$
$241$	94.7516			0.393160			0.196580	+	0.980488i	$0.437016\pi$
$242$	−84.2049			−0.347954
$243$	74.1631	+	231.406i	0.305198	+	0.952289i
$244$	25.0896			0.102826
$245$		0			0
$246$	223.950	+	142.375i	0.910365	+	0.578761i
$247$		−	403.012i		−	1.63163i
$248$	−48.6906			−0.196333
$249$	149.478	−	235.122i	0.600311	−	0.944263i
$250$		0			0
$251$		−	46.8378i		−	0.186605i	−0.995638	−	0.0933023i	$-0.970258\pi$
$251$		−	46.8378i		−	0.186605i	0.995638	−	0.0933023i	$-0.0297423\pi$
$252$	−43.1235	+	20.2079i	−0.171125	+	0.0801901i
$253$		−	82.4012i		−	0.325696i
$254$			256.116i			1.00833i
$255$		0			0
$256$	16.0000			0.0625000
$257$	58.1337			0.226201			0.113101	−	0.993584i	$-0.463922\pi$
$257$	58.1337			0.226201			0.113101	+	0.993584i	$0.463922\pi$
$258$	−254.318	−	161.682i	−0.985731	−	0.626674i
$259$	−171.328			−0.661498
$260$		0			0
$261$	−379.136	+	177.665i	−1.45263	+	0.680708i
$262$		−	5.67707i		−	0.0216682i
$263$	372.471			1.41624			0.708121	−	0.706092i	$-0.249543\pi$
$263$	372.471			1.41624			0.708121	+	0.706092i	$0.249543\pi$
$264$	96.2155	+	61.1686i	0.364453	+	0.231699i
$265$		0			0
$266$		−	75.6115i		−	0.284254i
$267$	−13.5921	−	8.64111i	−0.0509067	−	0.0323637i
$268$			236.472i			0.882357i
$269$			198.582i			0.738221i	0.929385	+	0.369111i	$0.120338\pi$
$269$			198.582i			0.738221i	−0.929385	+	0.369111i	$0.879662\pi$
$270$		0			0
$271$	334.221			1.23329			0.616644	−	0.787242i	$-0.288492\pi$
$271$	334.221			1.23329			0.616644	+	0.787242i	$0.288492\pi$
$272$	67.4182			0.247861
$273$	−84.9253	+	133.584i	−0.311082	+	0.489318i
$274$	110.894			0.404721
$275$		0			0
$276$	−19.7410	+	31.0517i	−0.0715253	+	0.112506i
$277$		−	466.582i		−	1.68441i	−0.539156	−	0.842206i	$-0.681257\pi$
$277$		−	466.582i		−	1.68441i	0.539156	−	0.842206i	$-0.318743\pi$
$278$	58.0237			0.208718
$279$	65.7420	+	140.293i	0.235634	+	0.502842i
$280$		0			0
$281$			516.652i			1.83862i	0.393536	+	0.919309i	$0.371252\pi$
$281$			516.652i			1.83862i	−0.393536	+	0.919309i	$0.628748\pi$
$282$	−108.543	+	170.734i	−0.384905	+	0.605439i
$283$		−	476.620i		−	1.68417i	−0.539346	−	0.842084i	$-0.681328\pi$
$283$		−	476.620i		−	1.68417i	0.539346	−	0.842084i	$-0.318672\pi$
$284$		−	15.8944i		−	0.0559660i
$285$		0			0
$286$	378.964			1.32505
$287$	165.491			0.576623
$288$	−21.6032	−	46.1010i	−0.0750110	−	0.160073i
$289$	−4.92410			−0.0170384
$290$		0			0
$291$	21.7393	+	13.8207i	0.0747054	+	0.0474937i
$292$			146.428i			0.501466i
$293$	−169.952			−0.580041			−0.290021	−	0.957020i	$-0.593662\pi$
$293$	−169.952			−0.580041			−0.290021	+	0.957020i	$0.593662\pi$
$294$	−15.9334	+	25.0625i	−0.0541951	+	0.0852465i
$295$		0			0
$296$		−	183.157i		−	0.618775i
$297$	46.3359	−	359.817i	0.156013	−	1.21150i
$298$		−	31.1658i		−	0.104583i
$299$			122.303i			0.409041i
$300$		0			0
$301$	−187.932			−0.624359
$302$	−136.150			−0.450829
$303$	−98.2388	−	62.4549i	−0.324220	−	0.206122i
$304$	80.8321			0.265895
$305$		0			0
$306$	−91.0279	−	194.253i	−0.297477	−	0.634814i
$307$			312.115i			1.01666i	0.861162	+	0.508331i	$0.169737\pi$
$307$			312.115i			1.01666i	−0.861162	+	0.508331i	$0.830263\pi$
$308$	71.0997			0.230843
$309$	−21.4055	−	13.6084i	−0.0692733	−	0.0440402i
$310$		0			0
$311$			425.633i			1.36859i	0.729204	+	0.684297i	$0.239891\pi$
$311$			425.633i			1.36859i	−0.729204	+	0.684297i	$0.760109\pi$
$312$	−142.807	−	90.7889i	−0.457715	−	0.290990i
$313$			399.201i			1.27540i	0.770283	+	0.637702i	$0.220115\pi$
$313$			399.201i			1.27540i	−0.770283	+	0.637702i	$0.779885\pi$
$314$			30.5876i			0.0974128i
$315$		0			0
$316$	−216.342			−0.684627
$317$	237.853			0.750326			0.375163	−	0.926959i	$-0.377587\pi$
$317$	237.853			0.750326			0.375163	+	0.926959i	$0.377587\pi$
$318$	82.5003	−	129.769i	0.259435	−	0.408079i
$319$	625.098			1.95956
$320$		0			0
$321$	87.4794	−	137.601i	0.272521	−	0.428664i
$322$			22.9461i			0.0712611i
$323$	340.597			1.05448
$324$	−103.663	+	124.491i	−0.319947	+	0.384231i
$325$		0			0
$326$			316.570i			0.971075i
$327$	164.483	−	258.724i	0.503005	−	0.791205i
$328$			176.917i			0.539381i
$329$			126.166i			0.383483i
$330$		0			0
$331$	−300.437			−0.907665			−0.453832	−	0.891087i	$-0.649944\pi$
$331$	−300.437			−0.907665			−0.453832	+	0.891087i	$0.649944\pi$
$332$	185.743			0.559466
$333$	−527.734	+	247.299i	−1.58479	+	0.742639i
$334$	407.263			1.21935
$335$		0			0
$336$	−26.7929	−	17.0335i	−0.0797408	−	0.0506949i
$337$		−	19.8344i		−	0.0588558i	−0.999567	−	0.0294279i	$-0.990631\pi$
$337$		−	19.8344i		−	0.0588558i	0.999567	−	0.0294279i	$-0.00936855\pi$
$338$	−323.471			−0.957016
$339$	218.540	−	343.753i	0.644660	−	1.01402i
$340$		0			0
$341$		−	231.307i		−	0.678321i
$342$	−109.139	−	232.903i	−0.319121	−	0.681002i
$343$			18.5203i			0.0539949i
$344$		−	200.908i		−	0.584034i
$345$		0			0
$346$	−408.805			−1.18152
$347$	27.7575			0.0799929			0.0399965	−	0.999200i	$-0.487265\pi$
$347$	27.7575			0.0799929			0.0399965	+	0.999200i	$0.487265\pi$
$348$	−235.559	−	149.756i	−0.676894	−	0.430333i
$349$	−299.360			−0.857766			−0.428883	−	0.903360i	$-0.641093\pi$
$349$	−299.360			−0.857766			−0.428883	+	0.903360i	$0.641093\pi$
$350$		0			0
$351$	−68.7737	+	534.055i	−0.195936	+	1.52152i
$352$			76.0088i			0.215934i
$353$	−679.926			−1.92614			−0.963068	−	0.269259i	$-0.913221\pi$
$353$	−679.926			−1.92614			−0.963068	+	0.269259i	$0.913221\pi$
$354$	−8.92048	−	5.67116i	−0.0251991	−	0.0160202i
$355$		0			0
$356$		−	10.7375i		−	0.0301616i
$357$	−112.896	−	71.7729i	−0.316234	−	0.201045i
$358$		−	65.9164i		−	0.184124i
$359$		−	33.8301i		−	0.0942344i	−0.998889	−	0.0471172i	$-0.984997\pi$
$359$		−	33.8301i		−	0.0942344i	0.998889	−	0.0471172i	$-0.0150034\pi$
$360$		0			0
$361$	47.3645			0.131204
$362$	−195.287			−0.539466
$363$	−95.8334	+	150.742i	−0.264004	+	0.415266i
$364$	−105.529			−0.289915
$365$		0			0
$366$	28.5545	−	44.9149i	0.0780176	−	0.122718i
$367$			300.646i			0.819199i	0.912265	+	0.409599i	$0.134332\pi$
$367$			300.646i			0.819199i	−0.912265	+	0.409599i	$0.865668\pi$
$368$	−24.5304			−0.0666587
$369$	509.753	−	238.873i	1.38145	−	0.647352i
$370$		0			0
$371$		−	95.8948i		−	0.258476i
$372$	−55.4147	+	87.1649i	−0.148964	+	0.234314i
$373$			119.661i			0.320807i	0.987052	+	0.160403i	$0.0512795\pi$
$373$			119.661i			0.320807i	−0.987052	+	0.160403i	$0.948720\pi$
$374$			320.274i			0.856347i
$375$		0			0
$376$	−134.877			−0.358716
$377$	−927.796			−2.46100
$378$	−12.9031	+	100.197i	−0.0341351	+	0.265072i
$379$	−149.138			−0.393504			−0.196752	−	0.980453i	$-0.563039\pi$
$379$	−149.138			−0.393504			−0.196752	+	0.980453i	$0.563039\pi$
$380$		0			0
$381$	458.492	+	291.485i	1.20339	+	0.765052i
$382$			27.8786i			0.0729806i
$383$	−296.924			−0.775257			−0.387629	−	0.921816i	$-0.626706\pi$
$383$	−296.924			−0.775257			−0.387629	+	0.921816i	$0.626706\pi$
$384$	18.2096	−	28.6428i	0.0474207	−	0.0745907i
$385$		0			0
$386$		−	77.8705i		−	0.201737i
$387$	−578.878	+	271.265i	−1.49581	+	0.700944i
$388$			17.1737i			0.0442621i
$389$			542.557i			1.39475i	0.716708	+	0.697374i	$0.245648\pi$
$389$			542.557i			1.39475i	−0.716708	+	0.697374i	$0.754352\pi$
$390$		0			0
$391$	−103.362			−0.264353
$392$	−19.7990			−0.0505076
$393$	−10.1630	−	6.46105i	−0.0258599	−	0.0164403i
$394$	319.183			0.810109
$395$		0			0
$396$	219.005	−	102.627i	0.553043	−	0.259159i
$397$			598.546i			1.50767i	0.657062	+	0.753837i	$0.271799\pi$
$397$			598.546i			1.50767i	−0.657062	+	0.753837i	$0.728201\pi$
$398$	−265.136			−0.666171
$399$	−135.358	−	86.0533i	−0.339243	−	0.215672i
$400$		0			0
$401$		−	430.276i		−	1.07301i	−0.843898	−	0.536504i	$-0.819745\pi$
$401$		−	430.276i		−	1.07301i	0.843898	−	0.536504i	$-0.180255\pi$
$402$	423.326	+	269.128i	1.05305	+	0.669472i
$403$			343.316i			0.851901i
$404$		−	77.6072i		−	0.192097i
$405$		0			0
$406$	−174.070			−0.428743
$407$	870.098			2.13783
$408$	76.7285	−	120.691i	0.188060	−	0.295810i
$409$	680.639			1.66415			0.832077	−	0.554661i	$-0.187152\pi$
$409$	680.639			1.66415			0.832077	+	0.554661i	$0.187152\pi$
$410$		0			0
$411$	126.208	−	198.519i	0.307075	−	0.483015i
$412$		−	16.9100i		−	0.0410437i
$413$	−6.59191			−0.0159610
$414$	33.1209	+	70.6797i	0.0800021	+	0.170724i
$415$		0			0
$416$		−	112.815i		−	0.271191i
$417$	66.0366	−	103.873i	0.158361	−	0.249095i
$418$			383.997i			0.918653i
$419$			630.755i			1.50538i	0.658374	+	0.752691i	$0.271245\pi$
$419$			630.755i			1.50538i	−0.658374	+	0.752691i	$0.728755\pi$
$420$		0			0
$421$	174.563			0.414638			0.207319	−	0.978273i	$-0.433526\pi$
$421$	174.563			0.414638			0.207319	+	0.978273i	$0.433526\pi$
$422$	489.755			1.16056
$423$	182.111	+	388.623i	0.430522	+	0.918732i
$424$	102.516			0.241783
$425$		0			0
$426$	−28.4537	−	18.0893i	−0.0667928	−	0.0424632i
$427$		−	33.1905i		−	0.0777295i
$428$	108.703			0.253979
$429$	431.297	−	678.412i	1.00536	−	1.58138i
$430$		0			0
$431$			380.300i			0.882367i	0.897417	+	0.441183i	$0.145441\pi$
$431$			380.300i			0.882367i	−0.897417	+	0.441183i	$0.854559\pi$
$432$	−107.115	−	13.7940i	−0.247953	−	0.0319304i
$433$		−	673.009i		−	1.55429i	−0.629320	−	0.777146i	$-0.716666\pi$
$433$		−	673.009i		−	1.55429i	0.629320	−	0.777146i	$-0.283334\pi$
$434$			64.4117i			0.148414i
$435$		0			0
$436$	204.388			0.468780
$437$	−123.928			−0.283587
$438$	262.132	+	166.650i	0.598476	+	0.380478i
$439$	−227.303			−0.517775			−0.258888	−	0.965907i	$-0.583356\pi$
$439$	−227.303			−0.517775			−0.258888	+	0.965907i	$0.583356\pi$
$440$		0			0
$441$	26.7326	+	57.0471i	0.0606180	+	0.129358i
$442$		−	475.363i		−	1.07548i
$443$	−583.446			−1.31703			−0.658517	−	0.752566i	$-0.728816\pi$
$443$	−583.446			−1.31703			−0.658517	+	0.752566i	$0.728816\pi$
$444$	−327.884	−	208.451i	−0.738478	−	0.469484i
$445$		0			0
$446$			447.505i			1.00338i
$447$	−55.7923	−	35.4697i	−0.124815	−	0.0793506i
$448$		−	21.1660i		−	0.0472456i
$449$			513.491i			1.14363i	0.820382	+	0.571816i	$0.193761\pi$
$449$			513.491i			1.14363i	−0.820382	+	0.571816i	$0.806239\pi$
$450$		0			0
$451$	−840.453			−1.86353
$452$	271.560			0.600797
$453$	−154.952	+	243.733i	−0.342058	+	0.538043i
$454$	−11.0105			−0.0242522
$455$		0			0
$456$	91.9948	−	144.704i	0.201743	−	0.317333i
$457$		−	639.473i		−	1.39928i	−0.714493	−	0.699642i	$-0.753343\pi$
$457$		−	639.473i		−	1.39928i	0.714493	−	0.699642i	$-0.246657\pi$
$458$	172.383			0.376382
$459$	−451.346	−	58.1227i	−0.983324	−	0.126629i
$460$		0			0
$461$		−	482.830i		−	1.04735i	−0.851917	−	0.523677i	$-0.824560\pi$
$461$		−	482.830i		−	1.04735i	0.851917	−	0.523677i	$-0.175440\pi$
$462$	80.9184	−	127.281i	0.175148	−	0.275500i
$463$		−	328.508i		−	0.709521i	−0.934957	−	0.354760i	$-0.884562\pi$
$463$		−	328.508i		−	0.709521i	0.934957	−	0.354760i	$-0.115438\pi$
$464$		−	186.088i		−	0.401053i
$465$		0			0
$466$	113.360			0.243262
$467$	−212.890			−0.455868			−0.227934	−	0.973677i	$-0.573197\pi$
$467$	−212.890			−0.455868			−0.227934	+	0.973677i	$0.573197\pi$
$468$	−325.057	+	152.323i	−0.694565	+	0.325477i
$469$	312.823			0.666999
$470$		0			0
$471$	54.7573	+	34.8117i	0.116257	+	0.0739102i
$472$		−	7.04705i		−	0.0149302i
$473$	954.423			2.01781
$474$	−246.219	+	387.291i	−0.519449	+	0.817070i
$475$		0			0
$476$		−	89.1859i		−	0.187365i
$477$	−138.417	−	295.380i	−0.290182	−	0.619246i
$478$			164.410i			0.343954i
$479$			102.615i			0.214228i	0.994247	+	0.107114i	$0.0341610\pi$
$479$			102.615i			0.214228i	−0.994247	+	0.107114i	$0.965839\pi$
$480$		0			0
$481$	−1291.44			−2.68490
$482$	133.999			0.278006
$483$	41.0775	+	26.1149i	0.0850467	+	0.0540681i
$484$	−119.084			−0.246041
$485$		0			0
$486$	104.882	+	327.258i	0.215807	+	0.673370i
$487$		−	23.7100i		−	0.0486858i	−0.999704	−	0.0243429i	$-0.992251\pi$
$487$		−	23.7100i		−	0.0486858i	0.999704	−	0.0243429i	$-0.00774936\pi$
$488$	35.4821			0.0727092
$489$	566.717	+	360.288i	1.15893	+	0.736785i
$490$		0			0
$491$		−	163.277i		−	0.332540i	−0.986080	−	0.166270i	$-0.946828\pi$
$491$		−	163.277i		−	0.332540i	0.986080	−	0.166270i	$-0.0531723\pi$
$492$	316.713	+	201.349i	0.643725	+	0.409246i
$493$		−	784.109i		−	1.59048i
$494$		−	569.944i		−	1.15373i
$495$		0			0
$496$	−68.8590			−0.138829
$497$	−21.0263			−0.0423064
$498$	211.393	−	332.512i	0.424484	−	0.667695i
$499$	−311.153			−0.623553			−0.311776	−	0.950156i	$-0.600924\pi$
$499$	−311.153			−0.623553			−0.311776	+	0.950156i	$0.600924\pi$
$500$		0			0
$501$	463.505	−	729.074i	0.925161	−	1.45524i
$502$		−	66.2386i		−	0.131949i
$503$	−875.585			−1.74073			−0.870363	−	0.492411i	$-0.836116\pi$
$503$	−875.585			−1.74073			−0.870363	+	0.492411i	$0.836116\pi$
$504$	−60.9859	+	28.5783i	−0.121004	+	0.0567030i
$505$		0			0
$506$		−	116.533i		−	0.230302i
$507$	−368.142	+	579.071i	−0.726118	+	1.14215i
$508$			362.202i			0.712997i
$509$			151.027i			0.296713i	0.988934	+	0.148356i	$0.0473983\pi$
$509$			151.027i			0.296713i	−0.988934	+	0.148356i	$0.952602\pi$
$510$		0			0
$511$	193.706			0.379073
$512$	22.6274			0.0441942
$513$	−541.148	−	69.6871i	−1.05487	−	0.135842i
$514$	82.2135			0.159948
$515$		0			0
$516$	−359.661	−	228.653i	−0.697017	−	0.443125i
$517$		−	640.741i		−	1.23934i
$518$	−242.294			−0.467750
$519$	−465.260	+	731.833i	−0.896454	+	1.41008i
$520$		0			0
$521$			974.956i			1.87132i	0.352906	+	0.935659i	$0.385193\pi$
$521$			974.956i			1.87132i	−0.352906	+	0.935659i	$0.614807\pi$
$522$	−536.179	+	251.256i	−1.02716	+	0.481334i
$523$		−	103.233i		−	0.197386i	−0.995118	−	0.0986932i	$-0.968534\pi$
$523$		−	103.233i		−	0.197386i	0.995118	−	0.0986932i	$-0.0314662\pi$
$524$		−	8.02858i		−	0.0153217i
$525$		0			0
$526$	526.754			1.00143
$527$	−290.147			−0.550563
$528$	136.069	+	86.5054i	0.257707	+	0.163836i
$529$	−491.391			−0.928906
$530$		0			0
$531$	−20.3048	+	9.51491i	−0.0382387	+	0.0179189i
$532$		−	106.931i		−	0.200998i
$533$	1247.44			2.34040
$534$	−19.2221	−	12.2204i	−0.0359965	−	0.0228846i
$535$		0			0
$536$			334.421i			0.623920i
$537$	−118.002	−	75.0193i	−0.219743	−	0.139701i
$538$			280.837i			0.522001i
$539$		−	94.0561i		−	0.174501i
$540$		0			0
$541$	−195.027			−0.360493			−0.180247	−	0.983621i	$-0.557690\pi$
$541$	−195.027			−0.360493			−0.180247	+	0.983621i	$0.557690\pi$
$542$	472.660			0.872067
$543$	−222.255	+	349.598i	−0.409310	+	0.643826i
$544$	95.3437			0.175264
$545$		0			0
$546$	−120.102	+	188.916i	−0.219968	+	0.346000i
$547$		−	340.245i		−	0.622019i	−0.950407	−	0.311010i	$-0.899333\pi$
$547$		−	340.245i		−	0.622019i	0.950407	−	0.311010i	$-0.100667\pi$
$548$	156.827			0.286181
$549$	−47.9079	−	102.235i	−0.0872639	−	0.186221i
$550$		0			0
$551$		−	940.120i		−	1.70621i
$552$	−27.9180	+	43.9137i	−0.0505760	+	0.0795539i
$553$			286.194i			0.517530i
$554$		−	659.847i		−	1.19106i
$555$		0			0
$556$	82.0579			0.147586
$557$	211.476			0.379669			0.189834	−	0.981816i	$-0.439205\pi$
$557$	211.476			0.379669			0.189834	+	0.981816i	$0.439205\pi$
$558$	92.9732	+	198.404i	0.166619	+	0.355563i
$559$	−1416.59			−2.53416
$560$		0			0
$561$	573.346	+	364.503i	1.02201	+	0.649737i
$562$			730.656i			1.30010i
$563$	265.804			0.472120			0.236060	−	0.971738i	$-0.424144\pi$
$563$	265.804			0.472120			0.236060	+	0.971738i	$0.424144\pi$
$564$	−153.503	+	241.454i	−0.272169	+	0.428110i
$565$		0			0
$566$		−	674.042i		−	1.19089i
$567$	164.686	+	137.133i	0.290452	+	0.241857i
$568$		−	22.4780i		−	0.0395740i
$569$		−	211.136i		−	0.371066i	−0.982638	−	0.185533i	$-0.940599\pi$
$569$		−	211.136i		−	0.371066i	0.982638	−	0.185533i	$-0.0594011\pi$
$570$		0			0
$571$	701.534			1.22861			0.614303	−	0.789070i	$-0.289437\pi$
$571$	701.534			1.22861			0.614303	+	0.789070i	$0.289437\pi$
$572$	535.935			0.936950
$573$	49.9076	+	31.7285i	0.0870988	+	0.0553727i
$574$	234.039			0.407734
$575$		0			0
$576$	−30.5515	−	65.1967i	−0.0530408	−	0.113189i
$577$		−	636.245i		−	1.10268i	−0.834281	−	0.551339i	$-0.814117\pi$
$577$		−	636.245i		−	1.10268i	0.834281	−	0.551339i	$-0.185883\pi$
$578$	−6.96374			−0.0120480
$579$	−139.402	−	88.6242i	−0.240763	−	0.153064i
$580$		0			0
$581$		−	245.714i		−	0.422916i
$582$	30.7440	+	19.5454i	0.0528247	+	0.0335831i
$583$			487.007i			0.835346i
$584$			207.081i			0.354590i
$585$		0			0
$586$	−240.349			−0.410151
$587$	183.730			0.312998			0.156499	−	0.987678i	$-0.449979\pi$
$587$	183.730			0.312998			0.156499	+	0.987678i	$0.449979\pi$
$588$	−22.5332	+	35.4437i	−0.0383217	+	0.0602784i
$589$	−347.876			−0.590621
$590$		0			0
$591$	363.261	−	571.394i	0.614655	−	0.966825i
$592$		−	259.024i		−	0.437540i
$593$	383.317			0.646403			0.323202	−	0.946330i	$-0.395241\pi$
$593$	383.317			0.646403			0.323202	+	0.946330i	$0.395241\pi$
$594$	65.5289	−	508.858i	0.110318	−	0.856663i
$595$		0			0
$596$		−	44.0751i		−	0.0739515i
$597$	−301.751	+	474.641i	−0.505445	+	0.795043i
$598$			172.963i			0.289236i
$599$		−	508.749i		−	0.849331i	−0.905350	−	0.424666i	$-0.860392\pi$
$599$		−	508.749i		−	0.849331i	0.905350	−	0.424666i	$-0.139608\pi$
$600$		0			0
$601$	−268.140			−0.446157			−0.223079	−	0.974800i	$-0.571611\pi$
$601$	−268.140			−0.446157			−0.223079	+	0.974800i	$0.571611\pi$
$602$	−265.776			−0.441489
$603$	963.573	−	451.535i	1.59796	−	0.748814i
$604$	−192.546			−0.318784
$605$		0			0
$606$	−138.931	−	88.3246i	−0.229258	−	0.145750i
$607$			553.549i			0.911942i	0.889995	+	0.455971i	$0.150708\pi$
$607$			553.549i			0.911942i	−0.889995	+	0.455971i	$0.849292\pi$
$608$	114.314			0.188016
$609$	−198.108	+	311.616i	−0.325301	+	0.511684i
$610$		0			0
$611$			951.014i			1.55649i
$612$	−128.733	−	274.715i	−0.210348	−	0.448881i
$613$		−	1059.92i		−	1.72907i	−0.502574	−	0.864534i	$-0.667614\pi$
$613$		−	1059.92i		−	1.72907i	0.502574	−	0.864534i	$-0.332386\pi$
$614$			441.398i			0.718889i
$615$		0			0
$616$	100.550			0.163231
$617$	−767.572			−1.24404			−0.622020	−	0.783002i	$-0.713688\pi$
$617$	−767.572			−1.24404			−0.622020	+	0.783002i	$0.713688\pi$
$618$	−30.2719	−	19.2452i	−0.0489836	−	0.0311411i
$619$	253.548			0.409608			0.204804	−	0.978803i	$-0.434344\pi$
$619$	253.548			0.409608			0.204804	+	0.978803i	$0.434344\pi$
$620$		0			0
$621$	164.224	+	21.1482i	0.264451	+	0.0340551i
$622$			601.935i			0.967742i
$623$	−14.2044			−0.0228001
$624$	−201.960	−	128.395i	−0.323653	−	0.205761i
$625$		0			0
$626$			564.556i			0.901847i
$627$	687.423	+	437.026i	1.09637	+	0.697011i
$628$			43.2574i			0.0688813i
$629$		−	1091.43i		−	1.73519i
$630$		0			0
$631$	906.659			1.43686			0.718430	−	0.695599i	$-0.244861\pi$
$631$	906.659			1.43686			0.718430	+	0.695599i	$0.244861\pi$
$632$	−305.954			−0.484105
$633$	557.388	−	876.747i	0.880550	−	1.38507i
$634$	336.375			0.530560
$635$		0			0
$636$	116.673	−	183.521i	0.183448	−	0.288556i
$637$			139.602i			0.219155i
$638$	884.022			1.38561
$639$	−64.7662	+	30.3498i	−0.101356	+	0.0474957i
$640$		0			0
$641$		−	274.632i		−	0.428444i	−0.976785	−	0.214222i	$-0.931278\pi$
$641$		−	274.632i		−	0.428444i	0.976785	−	0.214222i	$-0.0687215\pi$
$642$	123.715	−	194.598i	0.192702	−	0.303111i
$643$			330.746i			0.514380i	0.966361	+	0.257190i	$0.0827965\pi$
$643$			330.746i			0.514380i	−0.966361	+	0.257190i	$0.917203\pi$
$644$			32.4507i			0.0503892i
$645$		0			0
$646$	481.677			0.745630
$647$	1040.01			1.60743			0.803717	−	0.595012i	$-0.202853\pi$
$647$	1040.01			1.60743			0.803717	+	0.595012i	$0.202853\pi$
$648$	−146.601	+	176.057i	−0.226237	+	0.271693i
$649$	33.4774			0.0515830
$650$		0			0
$651$	115.308	+	73.3068i	0.177125	+	0.112606i
$652$			447.698i			0.686654i
$653$	154.399			0.236445			0.118223	−	0.992987i	$-0.462280\pi$
$653$	154.399			0.236445			0.118223	+	0.992987i	$0.462280\pi$
$654$	232.614	−	365.891i	0.355678	−	0.559466i
$655$		0			0
$656$			250.198i			0.381400i
$657$	596.664	−	279.600i	0.908165	−	0.425571i
$658$			178.426i			0.271164i
$659$		−	1001.79i		−	1.52016i	−0.649830	−	0.760080i	$-0.725160\pi$
$659$		−	1001.79i		−	1.52016i	0.649830	−	0.760080i	$-0.274840\pi$
$660$		0			0
$661$	1000.37			1.51342			0.756711	−	0.653749i	$-0.226805\pi$
$661$	1000.37			1.51342			0.756711	+	0.653749i	$0.226805\pi$
$662$	−424.882			−0.641816
$663$	−850.985	−	541.010i	−1.28354	−	0.816003i
$664$	262.680			0.395602
$665$		0			0
$666$	−746.328	+	349.733i	−1.12061	+	0.525125i
$667$			285.301i			0.427738i
$668$	575.957			0.862212
$669$	801.114	+	509.305i	1.19748	+	0.761293i
$670$		0			0
$671$			168.560i			0.251207i
$672$	−37.8909	−	24.0890i	−0.0563853	−	0.0358467i
$673$		−	564.565i		−	0.838878i	−0.907784	−	0.419439i	$-0.862227\pi$
$673$		−	564.565i		−	0.838878i	0.907784	−	0.419439i	$-0.137773\pi$
$674$		−	28.0501i		−	0.0416174i
$675$		0			0
$676$	−457.457			−0.676712
$677$	401.550			0.593131			0.296566	−	0.955013i	$-0.404159\pi$
$677$	401.550			0.593131			0.296566	+	0.955013i	$0.404159\pi$
$678$	309.062	−	486.141i	0.455844	−	0.717022i
$679$	22.7187			0.0334590
$680$		0			0
$681$	−12.5310	+	19.7108i	−0.0184009	+	0.0289439i
$682$		−	327.118i		−	0.479645i
$683$	860.803			1.26033			0.630163	−	0.776463i	$-0.282988\pi$
$683$	860.803			1.26033			0.630163	+	0.776463i	$0.282988\pi$
$684$	−154.346	−	329.374i	−0.225653	−	0.481541i
$685$		0			0
$686$			26.1916i			0.0381802i
$687$	196.189	−	308.596i	0.285573	−	0.449193i
$688$		−	284.127i		−	0.412975i
$689$		−	722.835i		−	1.04911i
$690$		0			0
$691$	−40.0935			−0.0580224			−0.0290112	−	0.999579i	$-0.509236\pi$
$691$	−40.0935			−0.0580224			−0.0290112	+	0.999579i	$0.509236\pi$
$692$	−578.137			−0.835458
$693$	−135.763	−	289.717i	−0.195906	−	0.418062i
$694$	39.2551			0.0565635
$695$		0			0
$696$	−333.131	−	211.787i	−0.478637	−	0.304291i
$697$			1054.25i			1.51255i
$698$	−423.360			−0.606532
$699$	129.015	−	202.935i	0.184571	−	0.290321i
$700$		0			0
$701$			888.946i			1.26811i	0.773287	+	0.634056i	$0.218611\pi$
$701$			888.946i			1.26811i	−0.773287	+	0.634056i	$0.781389\pi$
$702$	−97.2606	+	755.267i	−0.138548	+	1.07588i
$703$		−	1308.59i		−	1.86144i
$704$			107.493i			0.152688i
$705$		0			0
$706$	−961.560			−1.36198
$707$	−102.665			−0.145212
$708$	−12.6155	−	8.02023i	−0.0178185	−	0.0113280i
$709$	−642.421			−0.906094			−0.453047	−	0.891487i	$-0.649663\pi$
$709$	−642.421			−0.906094			−0.453047	+	0.891487i	$0.649663\pi$
$710$		0			0
$711$	413.099	+	881.550i	0.581011	+	1.23987i
$712$		−	15.1852i		−	0.0213275i
$713$	105.571			0.148066
$714$	−159.659	−	101.502i	−0.223611	−	0.142160i
$715$		0			0
$716$		−	93.2199i		−	0.130195i
$717$	294.323	+	187.114i	0.410492	+	0.260969i
$718$		−	47.8430i		−	0.0666338i
$719$		−	268.325i		−	0.373192i	−0.982437	−	0.186596i	$-0.940254\pi$
$719$		−	268.325i		−	0.373192i	0.982437	−	0.186596i	$-0.0597456\pi$
$720$		0			0
$721$	−22.3698			−0.0310261
$722$	66.9835			0.0927750
$723$	152.504	−	239.882i	0.210932	−	0.331787i
$724$	−276.177			−0.381460
$725$		0			0
$726$	−135.529	+	213.181i	−0.186679	+	0.293638i
$727$		−	23.6995i		−	0.0325991i	−0.999867	−	0.0162995i	$-0.994811\pi$
$727$		−	23.6995i		−	0.0325991i	0.999867	−	0.0162995i	$-0.00518853\pi$
$728$	−149.241			−0.205001
$729$	705.216	+	184.693i	0.967374	+	0.253351i
$730$		0			0
$731$		−	1197.21i		−	1.63777i
$732$	40.3821	−	63.5193i	0.0551668	−	0.0867749i
$733$			308.228i			0.420502i	0.977647	+	0.210251i	$0.0674282\pi$
$733$			308.228i			0.420502i	−0.977647	+	0.210251i	$0.932572\pi$
$734$			425.178i			0.579261i
$735$		0			0
$736$	−34.6912			−0.0471348
$737$	−1588.69			−2.15561
$738$	720.900	−	337.817i	0.976830	−	0.457747i
$739$	−916.303			−1.23992			−0.619961	−	0.784632i	$-0.712852\pi$
$739$	−916.303			−1.23992			−0.619961	+	0.784632i	$0.712852\pi$
$740$		0			0
$741$	−1020.30	−	648.652i	−1.37692	−	0.875374i
$742$		−	135.616i		−	0.182770i
$743$	−1037.07			−1.39579			−0.697896	−	0.716199i	$-0.745880\pi$
$743$	−1037.07			−1.39579			−0.697896	+	0.716199i	$0.745880\pi$
$744$	−78.3682	+	123.270i	−0.105334	+	0.165685i
$745$		0			0
$746$			169.226i			0.226845i
$747$	−354.670	−	756.862i	−0.474792	−	1.01320i
$748$			452.935i			0.605528i
$749$		−	143.800i		−	0.191990i
$750$		0			0
$751$	−16.8752			−0.0224703			−0.0112352	−	0.999937i	$-0.503576\pi$
$751$	−16.8752			−0.0224703			−0.0112352	+	0.999937i	$0.503576\pi$
$752$	−190.745			−0.253650
$753$	−118.579	−	75.3860i	−0.157475	−	0.100114i
$754$	−1312.10			−1.74019
$755$		0			0
$756$	−18.2477	+	141.700i	−0.0241371	+	0.187434i
$757$		−	478.309i		−	0.631848i	−0.948784	−	0.315924i	$-0.897685\pi$
$757$		−	478.309i		−	0.631848i	0.948784	−	0.315924i	$-0.102315\pi$
$758$	−210.913			−0.278249
$759$	−208.614	−	132.626i	−0.274854	−	0.174738i
$760$		0			0
$761$		−	1498.03i		−	1.96850i	−0.176790	−	0.984249i	$-0.556571\pi$
$761$		−	1498.03i		−	1.96850i	0.176790	−	0.984249i	$-0.443429\pi$
$762$	648.406	+	412.222i	0.850927	+	0.540973i
$763$		−	270.380i		−	0.354365i
$764$			39.4263i			0.0516051i
$765$		0			0
$766$	−419.913			−0.548190
$767$	−49.6885			−0.0647829
$768$	25.7522	−	40.5071i	0.0335315	−	0.0527436i
$769$	116.918			0.152038			0.0760192	−	0.997106i	$-0.475779\pi$
$769$	116.918			0.152038			0.0760192	+	0.997106i	$0.475779\pi$
$770$		0			0
$771$	93.5670	−	147.177i	0.121358	−	0.190891i
$772$		−	110.125i		−	0.142650i
$773$	−1151.33			−1.48943			−0.744713	−	0.667385i	$-0.767414\pi$
$773$	−1151.33			−1.48943			−0.744713	+	0.667385i	$0.767414\pi$
$774$	−818.658	+	383.627i	−1.05770	+	0.495642i
$775$		0			0
$776$			24.2873i			0.0312981i
$777$	−275.755	+	433.750i	−0.354897	+	0.558237i
$778$			767.291i			0.986235i
$779$			1264.00i			1.62260i
$780$		0			0
$781$	106.783			0.136726
$782$	−146.176			−0.186926
$783$	−160.431	+	1245.81i	−0.204893	+	1.59107i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	−14.3726	−	9.13731i	−0.0182857	−	0.0116251i
$787$			453.417i			0.576133i	0.957610	+	0.288066i	$0.0930124\pi$
$787$			453.417i			0.576133i	−0.957610	+	0.288066i	$0.906988\pi$
$788$	451.393			0.572833
$789$	599.498	−	942.983i	0.759819	−	1.19516i
$790$		0			0
$791$		−	359.240i		−	0.454160i
$792$	309.720	−	145.136i	0.391061	−	0.183253i
$793$		−	250.183i		−	0.315489i
$794$			846.472i			1.06609i
$795$		0			0
$796$	−374.959			−0.471054
$797$	−473.995			−0.594724			−0.297362	−	0.954765i	$-0.596107\pi$
$797$	−473.995			−0.594724			−0.297362	+	0.954765i	$0.596107\pi$
$798$	−191.425	−	121.698i	−0.239881	−	0.152503i
$799$	−803.731			−1.00592
$800$		0			0
$801$	−43.7533	+	20.5030i	−0.0546233	+	0.0255968i
$802$		−	608.502i		−	0.758731i
$803$	−983.747			−1.22509
$804$	598.673	+	380.604i	0.744619	+	0.473388i
$805$		0			0
$806$			485.522i			0.602385i
$807$	502.747	+	319.620i	0.622983	+	0.396059i
$808$		−	109.753i		−	0.135833i
$809$		−	875.429i		−	1.08211i	−0.840986	−	0.541056i	$-0.818025\pi$
$809$		−	875.429i		−	1.08211i	0.840986	−	0.541056i	$-0.181975\pi$
$810$		0			0
$811$	−764.492			−0.942653			−0.471326	−	0.881959i	$-0.656225\pi$
$811$	−764.492			−0.942653			−0.471326	+	0.881959i	$0.656225\pi$
$812$	−246.172			−0.303167
$813$	537.933	−	846.145i	0.661665	−	1.04077i
$814$	1230.50			1.51168
$815$		0			0
$816$	108.510	−	170.682i	0.132979	−	0.209169i
$817$		−	1435.41i		−	1.75693i
$818$	962.568			1.17673
$819$	201.505	+	430.009i	0.246037	+	0.525042i
$820$		0			0
$821$		−	531.214i		−	0.647032i	−0.946223	−	0.323516i	$-0.895135\pi$
$821$		−	531.214i		−	0.647032i	0.946223	−	0.323516i	$-0.104865\pi$
$822$	178.485	−	280.748i	0.217135	−	0.341543i
$823$		−	655.979i		−	0.797059i	−0.917156	−	0.398529i	$-0.869521\pi$
$823$		−	655.979i		−	0.797059i	0.917156	−	0.398529i	$-0.130479\pi$
$824$		−	23.9143i		−	0.0290223i
$825$		0			0
$826$	−9.32237			−0.0112862
$827$	1340.71			1.62118			0.810588	−	0.585617i	$-0.199148\pi$
$827$	1340.71			1.62118			0.810588	+	0.585617i	$0.199148\pi$
$828$	46.8400	+	99.9563i	0.0565701	+	0.120720i
$829$	−753.042			−0.908374			−0.454187	−	0.890906i	$-0.650070\pi$
$829$	−753.042			−0.908374			−0.454187	+	0.890906i	$0.650070\pi$
$830$		0			0
$831$	−1181.24	−	750.970i	−1.42147	−	0.903694i
$832$		−	159.545i		−	0.191761i
$833$	−117.982			−0.141635
$834$	93.3899	−	146.898i	0.111978	−	0.176137i
$835$		0			0
$836$			543.054i			0.649586i
$837$	460.991	+	59.3648i	0.550766	+	0.0709257i
$838$			892.023i			1.06447i
$839$		−	1123.90i		−	1.33957i	−0.742556	−	0.669784i	$-0.766387\pi$
$839$		−	1123.90i		−	1.33957i	0.742556	−	0.669784i	$-0.233613\pi$
$840$		0			0
$841$	−1323.30			−1.57349
$842$	246.869			0.293193
$843$	1308.00	+	831.558i	1.55161	+	0.986427i
$844$	692.617			0.820637
$845$		0			0
$846$	257.544	+	549.597i	0.304425	+	0.649641i
$847$			157.533i			0.185989i
$848$	144.979			0.170966
$849$	−1206.65	−	767.126i	−1.42127	−	0.903564i
$850$		0			0
$851$			397.122i			0.466653i
$852$	−40.2396	−	25.5822i	−0.0472296	−	0.0300260i
$853$			849.611i			0.996027i	0.867169	+	0.498014i	$0.165937\pi$
$853$			849.611i			0.996027i	−0.867169	+	0.498014i	$0.834063\pi$
$854$		−	46.9384i		−	0.0549630i
$855$		0			0
$856$	153.729			0.179590
$857$	−474.061			−0.553164			−0.276582	−	0.960990i	$-0.589202\pi$
$857$	−474.061			−0.553164			−0.276582	+	0.960990i	$0.589202\pi$
$858$	609.947	−	959.419i	0.710894	−	1.11820i
$859$	−357.378			−0.416039			−0.208020	−	0.978125i	$-0.566702\pi$
$859$	−357.378			−0.416039			−0.208020	+	0.978125i	$0.566702\pi$
$860$		0			0
$861$	266.359	−	418.972i	0.309361	−	0.486611i
$862$			537.826i			0.623928i
$863$	−39.7566			−0.0460680			−0.0230340	−	0.999735i	$-0.507333\pi$
$863$	−39.7566			−0.0460680			−0.0230340	+	0.999735i	$0.507333\pi$
$864$	−151.484	−	19.5076i	−0.175329	−	0.0225782i
$865$		0			0
$866$		−	951.778i		−	1.09905i
$867$	−7.92541	+	12.4663i	−0.00914119	+	0.0143787i
$868$			91.0918i			0.104945i
$869$		−	1453.45i		−	1.67256i
$870$		0			0
$871$	2357.99			2.70722
$872$	289.049			0.331478
$873$	69.9793	−	32.7927i	0.0801596	−	0.0375632i
$874$	−175.260			−0.200527
$875$		0			0
$876$	370.711	+	235.678i	0.423186	+	0.269039i
$877$		−	758.777i		−	0.865196i	−0.901587	−	0.432598i	$-0.857597\pi$
$877$		−	758.777i		−	0.865196i	0.901587	−	0.432598i	$-0.142403\pi$
$878$	−321.455			−0.366122
$879$	−273.540	+	430.266i	−0.311195	+	0.489495i
$880$		0			0
$881$			568.736i			0.645557i	0.946474	+	0.322779i	$0.104617\pi$
$881$			568.736i			0.645557i	−0.946474	+	0.322779i	$0.895383\pi$
$882$	37.8055	+	80.6768i	0.0428634	+	0.0914703i
$883$			38.0294i			0.0430684i	0.999768	+	0.0215342i	$0.00685508\pi$
$883$			38.0294i			0.0430684i	−0.999768	+	0.0215342i	$0.993145\pi$
$884$		−	672.265i		−	0.760481i
$885$		0			0
$886$	−825.118			−0.931284
$887$	−906.851			−1.02238			−0.511190	−	0.859468i	$-0.670795\pi$
$887$	−906.851			−1.02238			−0.511190	+	0.859468i	$0.670795\pi$
$888$	−463.698	−	294.794i	−0.522183	−	0.331975i
$889$	479.149			0.538975
$890$		0			0
$891$	−836.367	−	696.438i	−0.938683	−	0.781636i
$892$			632.868i			0.709494i
$893$	−963.646			−1.07911
$894$	−78.9022	−	50.1618i	−0.0882575	−	0.0561094i
$895$		0			0
$896$		−	29.9333i		−	0.0334077i
$897$	309.634	+	196.849i	0.345189	+	0.219452i
$898$			726.185i			0.808670i
$899$			800.866i			0.890841i
$900$		0			0
$901$	610.890			0.678013
$902$	−1188.58			−1.31772
$903$	−302.479	+	475.786i	−0.334971	+	0.526895i
$904$	384.044			0.424828
$905$		0			0
$906$	−219.136	+	344.691i	−0.241872	+	0.380454i
$907$			108.414i			0.119530i	0.998212	+	0.0597652i	$0.0190352\pi$
$907$			108.414i			0.119530i	−0.998212	+	0.0597652i	$0.980965\pi$
$908$	−15.5712			−0.0171489
$909$	−316.233	+	148.188i	−0.347891	+	0.163024i
$910$		0			0
$911$			348.871i			0.382954i	0.981497	+	0.191477i	$0.0613278\pi$
$911$			348.871i			0.382954i	−0.981497	+	0.191477i	$0.938672\pi$
$912$	130.100	−	204.642i	0.142654	−	0.224388i
$913$			1247.87i			1.36678i
$914$		−	904.352i		−	0.989444i
$915$		0			0
$916$	243.786			0.266142
$917$	−10.6208			−0.0115821
$918$	−638.299	−	82.1979i	−0.695315	−	0.0895402i
$919$	1186.93			1.29155			0.645773	−	0.763529i	$-0.276535\pi$
$919$	1186.93			1.29155			0.645773	+	0.763529i	$0.276535\pi$
$920$		0			0
$921$	790.180	+	502.354i	0.857959	+	0.545444i
$922$		−	682.825i		−	0.740591i
$923$	−158.492			−0.171714
$924$	114.436	−	180.003i	0.123848	−	0.194808i
$925$		0			0
$926$		−	464.581i		−	0.501707i
$927$	−68.9047	+	32.2891i	−0.0743309	+	0.0348318i
$928$		−	263.169i		−	0.283587i
$929$		−	515.060i		−	0.554424i	−0.960809	−	0.277212i	$-0.910589\pi$
$929$		−	515.060i		−	0.554424i	0.960809	−	0.277212i	$-0.0894105\pi$
$930$		0			0
$931$	−141.456			−0.151940
$932$	160.315			0.172012
$933$	1077.57	+	685.061i	1.15495	+	0.734256i
$934$	−301.072			−0.322347
$935$		0			0
$936$	−459.699	+	215.417i	−0.491132	+	0.230147i
$937$		−	489.541i		−	0.522456i	−0.965277	−	0.261228i	$-0.915873\pi$
$937$		−	489.541i		−	0.522456i	0.965277	−	0.261228i	$-0.0841274\pi$
$938$	442.398			0.471640
$939$	1010.66	+	642.520i	1.07631	+	0.684260i
$940$		0			0
$941$			833.933i			0.886220i	0.896467	+	0.443110i	$0.146125\pi$
$941$			833.933i			0.886220i	−0.896467	+	0.443110i	$0.853875\pi$
$942$	77.4385	+	49.2312i	0.0822065	+	0.0522624i
$943$		−	383.592i		−	0.406778i
$944$		−	9.96603i		−	0.0105572i
$945$		0			0
$946$	1349.76			1.42681
$947$	−854.924			−0.902771			−0.451385	−	0.892329i	$-0.649070\pi$
$947$	−854.924			−0.902771			−0.451385	+	0.892329i	$0.649070\pi$
$948$	−348.206	+	547.712i	−0.367306	+	0.577755i
$949$	1460.12			1.53859
$950$		0			0
$951$	382.828	−	602.171i	0.402553	−	0.633198i
$952$		−	126.128i		−	0.132487i
$953$	1564.07			1.64121			0.820603	−	0.571498i	$-0.193638\pi$
$953$	1564.07			1.64121			0.820603	+	0.571498i	$0.193638\pi$
$954$	−195.751	−	417.731i	−0.205189	−	0.437873i
$955$		0			0
$956$			232.511i			0.243212i
$957$	1006.10	−	1582.56i	1.05131	−	1.65366i
$958$			145.120i			0.151482i
$959$		−	207.463i		−	0.216332i
$960$		0			0
$961$	−664.653			−0.691626
$962$	−1826.37			−1.89851
$963$	−207.565	−	442.942i	−0.215540	−	0.459960i
$964$	189.503			0.196580
$965$		0			0
$966$	58.0924	+	36.9320i	0.0601371	+	0.0382319i
$967$			64.0844i			0.0662714i	0.999451	+	0.0331357i	$0.0105493\pi$
$967$			64.0844i			0.0662714i	−0.999451	+	0.0331357i	$0.989451\pi$
$968$	−168.410			−0.173977
$969$	548.196	−	862.288i	0.565733	−	0.889874i
$970$		0			0
$971$		−	400.825i		−	0.412796i	−0.978468	−	0.206398i	$-0.933826\pi$
$971$		−	400.825i		−	0.412796i	0.978468	−	0.206398i	$-0.0661742\pi$
$972$	148.326	+	462.812i	0.152599	+	0.476144i
$973$		−	108.552i		−	0.111565i
$974$		−	33.5310i		−	0.0344261i
$975$		0			0
$976$	50.1793			0.0514132
$977$	−1473.80			−1.50850			−0.754248	−	0.656590i	$-0.771998\pi$
$977$	−1473.80			−1.50850			−0.754248	+	0.656590i	$0.771998\pi$
$978$	801.459	+	509.524i	0.819488	+	0.520986i
$979$	72.1380			0.0736854
$980$		0			0
$981$	−390.273	−	832.839i	−0.397831	−	0.848970i
$982$		−	230.909i		−	0.235141i
$983$	1166.05			1.18622			0.593109	−	0.805122i	$-0.297900\pi$
$983$	1166.05			1.18622			0.593109	+	0.805122i	$0.297900\pi$
$984$	447.900	+	284.750i	0.455183	+	0.289380i
$985$		0			0
$986$		−	1108.90i		−	1.12464i
$987$	319.414	+	203.066i	0.323621	+	0.205741i
$988$		−	806.023i		−	0.815813i
$989$			435.609i			0.440454i
$990$		0			0
$991$	575.510			0.580736			0.290368	−	0.956915i	$-0.406222\pi$
$991$	575.510			0.580736			0.290368	+	0.956915i	$0.406222\pi$
$992$	−97.3813			−0.0981666
$993$	−483.557	+	760.614i	−0.486966	+	0.765976i
$994$	−29.7356			−0.0299151
$995$		0			0
$996$	298.955	−	470.243i	0.300156	−	0.472132i
$997$		−	304.683i		−	0.305600i	−0.988257	−	0.152800i	$-0.951171\pi$
$997$		−	304.683i		−	0.305600i	0.988257	−	0.152800i	$-0.0488290\pi$
$998$	−440.036			−0.440918
$999$	−223.310	+	1734.09i	−0.223534	+	1.73583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.c.449.25		32
3.2	odd	2	inner	1050.3.c.c.449.7		32
5.2	odd	4		210.3.e.a.71.10	yes	16
5.3	odd	4		1050.3.e.d.701.7		16
5.4	even	2	inner	1050.3.c.c.449.8		32
15.2	even	4		210.3.e.a.71.2	✓	16
15.8	even	4		1050.3.e.d.701.15		16
15.14	odd	2	inner	1050.3.c.c.449.26		32
20.7	even	4		1680.3.l.c.1121.14		16
60.47	odd	4		1680.3.l.c.1121.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.e.a.71.2	✓	16	15.2	even	4
210.3.e.a.71.10	yes	16	5.2	odd	4
1050.3.c.c.449.7		32	3.2	odd	2	inner
1050.3.c.c.449.8		32	5.4	even	2	inner
1050.3.c.c.449.25		32	1.1	even	1	trivial
1050.3.c.c.449.26		32	15.14	odd	2	inner
1050.3.e.d.701.7		16	5.3	odd	4
1050.3.e.d.701.15		16	15.8	even	4
1680.3.l.c.1121.13		16	60.47	odd	4
1680.3.l.c.1121.14		16	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(1.60951 - 2.53169i) q^{3} +2.00000 q^{4} +(2.27619 - 3.58035i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(-3.81894 - 8.14958i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(1.60951 - 2.53169i) q^{3} +2.00000 q^{4} +(2.27619 - 3.58035i) q^{6} -2.64575i q^{7} +2.82843 q^{8} +(-3.81894 - 8.14958i) q^{9} +13.4366i q^{11} +(3.21903 - 5.06339i) q^{12} -19.9431i q^{13} -3.74166i q^{14} +4.00000 q^{16} +16.8546 q^{17} +(-5.40079 - 11.5253i) q^{18} +20.2080 q^{19} +(-6.69823 - 4.25837i) q^{21} +19.0022i q^{22} -6.13260 q^{23} +(4.55239 - 7.16071i) q^{24} -28.2039i q^{26} +(-26.7789 - 3.44849i) q^{27} -5.29150i q^{28} -46.5221i q^{29} -17.2147 q^{31} +5.65685 q^{32} +(34.0173 + 21.6264i) q^{33} +23.8359 q^{34} +(-7.63787 - 16.2992i) q^{36} -64.7559i q^{37} +28.5785 q^{38} +(-50.4899 - 32.0987i) q^{39} +62.5496i q^{41} +(-9.47273 - 6.02225i) q^{42} -71.0317i q^{43} +26.8732i q^{44} -8.67280 q^{46} -47.6863 q^{47} +(6.43805 - 10.1268i) q^{48} -7.00000 q^{49} +(27.1276 - 42.6705i) q^{51} -39.8863i q^{52} +36.2448 q^{53} +(-37.8710 - 4.87690i) q^{54} -7.48331i q^{56} +(32.5251 - 51.1605i) q^{57} -65.7922i q^{58} -2.49151i q^{59} +12.5448 q^{61} -24.3453 q^{62} +(-21.5618 + 10.1040i) q^{63} +8.00000 q^{64} +(48.1077 + 30.5843i) q^{66} +118.236i q^{67} +33.7091 q^{68} +(-9.87050 + 15.5259i) q^{69} -7.94718i q^{71} +(-10.8016 - 23.0505i) q^{72} +73.2141i q^{73} -91.5787i q^{74} +40.4161 q^{76} +35.5499 q^{77} +(-71.4035 - 45.3945i) q^{78} -108.171 q^{79} +(-51.8315 + 62.2455i) q^{81} +88.4585i q^{82} +92.8713 q^{83} +(-13.3965 - 8.51674i) q^{84} -100.454i q^{86} +(-117.780 - 74.8779i) q^{87} +38.0044i q^{88} -5.36877i q^{89} -52.7646 q^{91} -12.2652 q^{92} +(-27.7073 + 43.5824i) q^{93} -67.4386 q^{94} +(9.10478 - 14.3214i) q^{96} +8.58686i q^{97} -9.89949 q^{98} +(109.503 - 51.3135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9	\( 32 q + 64 q^{4} + 32 q^{6} + 8 q^{9} + 128 q^{16} - 96 q^{19} + 56 q^{21} + 64 q^{24} - 320 q^{34} + 16 q^{36} - 312 q^{39} + 64 q^{46} - 224 q^{49} + 168 q^{51} + 64 q^{54} + 224 q^{61} + 256 q^{64} - 16 q^{69} - 192 q^{76} - 16 q^{79} - 248 q^{81} + 112 q^{84} - 112 q^{91} - 64 q^{94} + 128 q^{96} + 104 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 + 32 * q^6 + 8 * q^9 + 128 * q^16 - 96 * q^19 + 56 * q^21 + 64 * q^24 - 320 * q^34 + 16 * q^36 - 312 * q^39 + 64 * q^46 - 224 * q^49 + 168 * q^51 + 64 * q^54 + 224 * q^61 + 256 * q^64 - 16 * q^69 - 192 * q^76 - 16 * q^79 - 248 * q^81 + 112 * q^84 - 112 * q^91 - 64 * q^94 + 128 * q^96 + 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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